Results
Explained Variance
k=—Quick Interpretation
Loadings Table
Loadings Heatmap
Input Data
Example Data Table
| Variable A | Variable B | Variable C |
|---|---|---|
| 2.1 | 1.9 | 0.2 |
| 2.5 | 2.4 | 0.3 |
| 1.9 | 2.2 | 0.1 |
| 3.2 | 2.9 | 0.7 |
| 2.8 | 2.6 | 0.6 |
| 1.6 | 1.7 | 0.0 |
| 3.0 | 2.7 | 0.8 |
| 2.2 | 2.0 | 0.2 |
Formula Used
- Centering: x' = x − μ, where μ is the column mean.
- Standardizing: z = (x − μ) / σ, where σ is the column standard deviation.
- Covariance/Correlation matrix: S = (1/(n−1)) ZᵀZ.
- Eigen-decomposition: S v = λ v gives eigenvalues λ and eigenvectors v.
- Loadings: columns of V (eigenvectors) are the component loadings.
- Explained variance ratio: λᵢ / Σⱼ λⱼ.
- Varimax rotation (optional): maximizes loading variance per component with an orthogonal rotation.
How to Use This Calculator
- Paste a numeric table where rows are observations and columns are variables.
- Select the delimiter and indicate whether the first row has names.
- Choose centering and standardization based on your analysis goal.
- Set the number of components (k) you want to inspect.
- Optionally enable Varimax rotation for clearer separation.
- Press Submit to view loadings and explained variance.
- Use the export buttons to download CSV or PDF outputs.
PCA loadings summarize variable influence
Loadings are weights that build each principal component. They show which variables drive separation. Larger absolute values mean stronger influence. Signs indicate direction along the component. Use loadings to name components in clear business terms.
Clean inputs improve stable components
Use numeric columns with consistent formatting. Remove identifiers and text fields before analysis. Avoid constant variables with zero variance. Handle outliers using winsorizing or robust scaling when needed. More observations usually give smoother loading patterns and rankings.
Centering and scaling change the matrix
Centering subtracts each column mean from every value. Scaling divides by the column standard deviation. Covariance PCA preserves units and spread across variables. Correlation PCA balances variables with different scales. Choose scaling when units differ, like dollars and milliseconds.
Explained variance guides component selection
Eigenvalues measure variance captured by each component. The variance ratio equals eigenvalue divided by total variance. Many datasets capture 70 percent using two to three components. Use cumulative variance with domain sense. Add components if key variables still load weakly. A scree drop often marks diminishing returns after early components. Check component stability by rerunning with bootstrapped samples when decisions are high stakes. Use k that keeps noise low overall.
Heatmap highlights strong positive and negative loadings
The heatmap compares variables across components in one view. Repeated strong colors suggest related variables and shared drivers. Mixed signs suggest tradeoffs between groups. The highlight threshold confirms the largest absolute loadings quickly. Look for sparse patterns after rotation for easier interpretation.
Rotation and exports support reporting workflows
Varimax rotation can sharpen structure while keeping orthogonal components. It often makes interpretation easier for teams and reviewers. Download CSV for spreadsheets, QA checks, and versioned pipelines. Download PDF for audits, lessons, and stakeholder updates. Save the settings to reproduce results across experiments.
FAQs
What are PCA loadings in simple terms?
Loadings are weights that combine variables into a component. Larger absolute weights mean stronger contribution. Signs show direction. Together, they define each principal component axis.
Should I center and standardize my data?
Centering is usually recommended. Standardization is best when variables use different units or scales. If all variables share similar units and variances, covariance-based PCA can be appropriate.
How many components should I choose?
Start with components that explain most variance. Many users target 70% to 90% cumulative variance. Also check interpretability. Too many components can dilute meaning.
What does a negative loading mean?
A negative loading means the variable decreases as the component score increases. It indicates an opposite direction relationship. Absolute size still measures strength, not importance sign.
What does Varimax rotation change?
Varimax redistributes loadings across components while keeping axes orthogonal. It can create clearer, more separated loading patterns. It does not change total variance explained by the chosen subspace.
Can I export results for a report?
Yes. Use CSV for spreadsheets and automated workflows. Use PDF for sharing and archiving. Both exports reflect the selected k, scaling, and rotation settings.